To solve the equation \( x^2 - 529 = 0 \), follow these steps:

1. **Add 529 to both sides:**
   \[
   x^2 = 529
   \]

2. **Take the square root of both sides:**
   \[
   x = \pm \sqrt{529}
   \]

3. **Calculate the square root of 529:**
   \[
   \sqrt{529} = 23
   \]

So, the solutions are:
\[
x = 23 \quad \text{or} \quad x = -23
\]

Would you like more details or have any questions? 

Here are some related questions:
1. How do you solve quadratic equations in general?
2. What is the significance of the plus/minus sign in square root operations?
3. Can a quadratic equation have complex solutions?
4. How would you solve \( x^2 - 576 = 0 \)?
5. How do you graph the solutions to \( x^2 - 529 = 0 \)?

**Tip:** Remember, the square root of a number has two values: one positive and one negative.

Learn how to solve the quadratic equation x^2 - 529 = 0 with a detailed step-by-step solution. This problem covers quadratic equations and square roots, with an emphasis on solving equations involving perfect squares. Suitable for students in Grades 7-9.

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